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The geometric (p) distribution on {0, 1, 2, .. }. The geometric (p) distribution is often defined as a distribution on {0, 1, 2, .. .. } instead of { 1, 2, 3, . . .}. A random variable W has geometric (p) distribution on (0, 1, 2, . ..) if
P(W = k qkp (k = 0, 1, . . )
a) Show that this is the distribution of the number of failures before the first success in Bernoulli (p) trials.
b) Find P(W > k) (k = 0, 1, . . .)
c) Find E(W).
d) Find Vαr(W).
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